-2/5x+3=6/2x-13

Solution for -2/5x+3=6/2x-13 equation:

-2/5x+3=6/2x-13

We move all terms to the left:

-2/5x+3-(6/2x-13)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-13)!=0

x∈R


We get rid of parentheses

-2/5x-6/2x+13+3=0

We calculate fractions


(-4x)/10x^2+(-30x)/10x^2+13+3=0

We add all the numbers together, and all the variables

(-4x)/10x^2+(-30x)/10x^2+16=0

We multiply all the terms by the denominator


(-4x)+(-30x)+16*10x^2=0

Wy multiply elements

160x^2+(-4x)+(-30x)=0

We get rid of parentheses

160x^2-4x-30x=0

We add all the numbers together, and all the variables

160x^2-34x=0

a = 160; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·160·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*160}=\frac{0}{320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*160}=\frac{68}{320}
=17/80
$